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Local Communication

Example: Jacobi finite difference method

X(t+1)i,j=(4X(t)i,j+X(t)i-1,j+X(t)i+1,j+X(t)i,j-1+X(t)i,j+1)/(8)
for t = 0 to T-1
  send X(t)(i,j) to each neighbor
  receive from neighbors 
    X(t)(i-1,j), X(t)(i+1,j), 
    X(t)(i,j-1), X(t)(i,j+1)
  compute X(t+1)(i,j)
end

Easy parallelization, but many iterations.

Improvement: Gauss-Seidel strategy

X(t+1)i,j=(4X(t)i,j+X(t+1)i-1,j+X(t)i+1,j+X(t+1)i,j-1+X(t)i,j+1)/(8)

Elements are updated in a particular order.

(See Foster, Figures 2.4 and 2.5)


Author: Wolfgang Schreiner
Last Modification: October 13, 1997

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